# Autoregressive Conditional Poisson Model – I

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Modeling the time series of count outcome is of interest in the operational risk while forecasting the frequency of losses. Below is an example showing how to estimate a simple ACP(1, 1) model, e.g. Autoregressive Conditional Poisson, without covariates with **ACP** package.

library(acp) ### acp(1, 1) without covariates ### mdl <- acp(y ~ -1, data = cnt) summary(mdl) # acp.formula(formula = y ~ -1, data = cnt) # # Estimate StdErr t.value p.value # a 0.632670 0.169027 3.7430 0.0002507 *** # b 0.349642 0.067414 5.1865 6.213e-07 *** # c 0.184509 0.134154 1.3753 0.1708881 ### generate predictions ### f <- predict(mdl) pred <- data.frame(yhat = f, cnt) tail(pred, 5) # yhat y # 164 1.5396921 1 # 165 1.2663993 0 # 166 0.8663321 1 # 167 1.1421586 3 # 168 1.8923355 6 ### calculate predictions manually ### pv167 <- mdl$coef[1] + mdl$coef[2] * pred$y[166] + mdl$coef[3] * pred$yhat[166] # [1] 1.142159 pv168 <- mdl$coef[1] + mdl$coef[2] * pred$y[167] + mdl$coef[3] * pred$yhat[167] # [1] 1.892336 plot.ts(pred, main = "Predictions")

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